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Re: Integral of radial solution (hydrogen atom) is not evaluated

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91535] Re: Integral of radial solution (hydrogen atom) is not evaluated
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 25 Aug 2008 06:57:15 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <g8lp87$ih2$1@smc.vnet.net> <g8o85j$l6c$1@smc.vnet.net> <g8tsq9$nv0$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

I don't know, but I expect that Mathematica uses
a "special extension" of Laguerre polynomials
Try

Plot3D[
  LaguerreL[n, l, 1], {n, 0, 5}, {l, 0, 5}]

For this special extension (real n and real l and l>n)
the orthogonal relation does not hold.

Regards
   Jens

Gehricht at googlemail.com wrote:
> Hi!
> 
>> and Mathematica can't evaluate
>> Integrate[
>>   LaguerreL[n1, l1, r]*LaguerreL[n2, l2, r]*Exp[-r], {r, 0, Infinity}]
>>
>> or
>>
>> Integrate[
>>   LaguerreL[n, l, r]*LaguerreL[n, l, r]*Exp[-r], {r, 0, Infinity}]
> 
> Is there any special reason for that?
> But thank you for the information!
> With thanks
> Wolfgang
> 


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